Complementing information about the number of connected components and holes in data that persistent homology can provide, \(\alpha \) -shapes, a concept from computational geometry, are a flexible means of characterizing the overall shape of data [1]}. A generalization of the convex hull rigorously defined by Edelsbrunner et al. [2]}, \(\alpha \) -shapes have been applied to reconstruct surfaces [3]}, [4]}, as well as estimate perimeter [5]}, surface curvature [6]}, shape complexity [7]}, and volume [8]}. For example, \(\alpha \) -shapes have been used in structural biology [8]} to better understand the shape of protein structures [10]}. Like persistent homology, \(\alpha \) -shapes lend themselves to point-cloud data (i.e., cell coordinates in our case study) and provide information about shape. They also naturally involve the choice of a hyper-parameter \(\alpha \) , and this inherent flexibility makes them suitable for our study.
